Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer

Abstract

We reduce the question about whether the Brauer-Manin obstruction to weak approximation for homogeneous spaces is the only obstruction to the "simpler" question of the particular case of homogeneous spaces of ${\mathrm{SL}}_n$ with finite stabilizer. We also give unconditional results based on the few known results on finite stabilizers.

16 pages. Final version. Slight modifications suggested by the referee added (including the title and Lemma 6)

References in corpus (1)

• Pathologies of the Brauer-Manin obstruction

Cited by in corpus (2)

• Zéro-cycles sur les espaces homogènes et problème de Galois inverse
• Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis (The Hasse principle for homogeneous spaces: reduction to the case of finite stabilizers)